Figure 1: Given a watertight surface (a), the well-known medial axis transform (b) often produces too complex of a structure to be of practical use. Our skeletonization algorithm can produce intermediate meso-skeletons (c), which contain medial sheets where needed and curves where appropriate, while converging to a medially centered curve skeleton output (d). AbstractInspired by recent developments in contraction-based curve skeleton extraction, we formulate the skeletonization problem via mean curvature flow (MCF). While the classical application of MCF is surface fairing, we take advantage of its area-minimizing characteristic to drive the curvature flow towards the extreme so as to collapse the input mesh geometry and obtain a skeletal structure. By analyzing the differential characteristics of the flow, we reveal that MCF locally increases shape anisotropy. This justifies the use of curvature motion for skeleton computation, and leads to the generation of what we call "mean curvature skeletons". To obtain a stable and efficient discretization, we regularize the surface mesh by performing local remeshing via edge splits and collapses. Simplifying mesh connectivity throughout the motion leads to more efficient computation and avoids numerical instability arising from degeneracies in the triangulation. In addition, the detection of collapsed geometry is facilitated by working with simplified mesh connectivity and monitoring potential non-manifold edge collapses. With topology simplified throughout the flow, minimal post-processing is required to convert the collapsed geometry to a curve. Formulating skeletonization via MCF allows us to incorporate external energy terms easily, resulting in a constrained flow. We define one such energy term using the Voronoi medial skeleton and obtain a medially centred curve skeleton. We call the intermediate results of our skeletonization motion meso-skeletons; these consist of a mixture of curves and surface sheets as appropriate to the local 3D geometry they capture.
Accurate depth estimation from images is a fundamental task in many applications including scene understanding and reconstruction. Existing solutions for depth estimation often produce blurry approximations of low resolution. This paper presents a convolutional neural network for computing a high-resolution depth map given a single RGB image with the help of transfer learning. Following a standard encoder-decoder architecture, we leverage features extracted using high performing pre-trained networks when initializing our encoder along with augmentation and training strategies that lead to more accurate results. We show how, even for a very simple decoder, our method is able to achieve detailed high-resolution depth maps. Our network, with fewer parameters and training iterations, outperforms state-of-the-art on two datasets and also produces qualitatively better results that capture object boundaries more faithfully. Code and corresponding pre-trained weights are made publicly available 1 .
We introduce an algorithm for generating novel 3D models via topology-varying shape blending. Given a source and a target shape, our method blends them topologically and geometrically, producing continuous series of in-betweens as new shape creations. The blending operations are defined on a spatio-structural graph composed of medial curves and sheets. Such a shape abstraction is structure-oriented, part-aware, and facilitates topology manipulations. Fundamental topological operations including split and merge are realized by allowing one-to-many correspondences between the source and the target. Multiple blending paths are sampled and presented in an interactive, exploratory tool for creative 3D modeling. We show a variety of topology-varying 3D shapes generated via continuous structural blending between man-made shapes exhibiting complex topological differences, in real time.
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